For Verizon Note 2, I highly recommend JellyBeans ROM (build 21 is the current one), CleanROM, or Liquidsmooth. I've tried a few AOSP ROMS, and each has compromised the performance of the device in one way or another. And with AOSP ROMS, you usually lose stock TouchWiz features on the Note like S-Pen and multi-view windows, which are what I love about the Note. There are workarounds in AOSP ROMS, but none of them are stock features, and in my opinion do not jive well with the way the device was meant to work. JellyBeans by beanstown has been the best ROM I think I've ever had on any device. It offers enough customizations to keep me happy, and it allows you to go with an AOSP look and feel to get rid of the hideous (to me) TouchWiz color scheme. Not a single freeze or random reboot, absolutely zero issues for me with this ROM.
Updated by lpt2569, Sep 11 '13 @ 11:20 AM.